Insight into band structures for out-of-plane propagation of a 2D dispersive photonic crystal: the dispersive photonic crystal iterative method

A study of the band structures of a two-dimensional dispersive photonic crystal for out-of-plane propagation along with the dispersive photonic crystal iterative method are presented. In these calculations, the proposed method uses the plane wave expansion method as the foundation. The photonic crystal is a square array of circular cross-sectional dispersive MgO Lorentz single-pole rods. The band structures were calculated starting at the high symmetry points 0, X, and M as a function of the oblique component of the propagation wave vector. The method used is discussed in detail, and a simple equation is presented for straightforward analytical calculations of points of the frequency bands in the transparency window, where the dielectric constant equals that of vacuum.